\section{Reinsurance - How PI Can Eliminate Risk and Lock In Profits}
\label{sec:Reinsurance-HowPICanEliminateRiskandLockInProfits}

Although $PI$ cannot adequately compensate smaller, less efficient insurers (risk assuming health care providers), $PI$ can lock in profits and eliminate risk by passing its claims costs to more efficient insurers, such as $NHI$ and $B$. If an insurer with 9,000,000 policyholders assumes all 1,000,000 of $PI$'s policyholders' it will be the same size as Insurer $B$, and will have the same standard error, $\sigma_{e_{10,000,000}}$ = 0.015811.

Likewise, if an insurer with 308,000,000 policyholders assumes all 1,000,000 of $PI$'s policyholders' it will be the same size as $NHI$, and will have the same standard error, $\sigma_{e_{309,000,000}}$ = 0.002844. Because both these insurers are larger, more efficient insurers they can each assume $PI$'s claims cost liabilities, accept less than 85\% of $PI$'s premium revenues to manage these risks, eliminating all of $PI$'s risk exposure, and meet, or exceed, $PI$'s pre-transfer probabilities of earning profits of at least 5\%, or avoiding operating losses, on their entire portfolios.

\subsection{Profit Adjusted Risk Premiums - PI Transfers Insurance Risks To B Or NHI}
 \label{sec:ProfitAdjustedPremiums-PITransfersRiskstoInsurerBorNHI}

$B$'s probability, $\Phi_{B}$(0.765811 = PLR + 1 * 0.015811) is 0.8413, $PI$'s probability of profits of at least 5\%. $B$ can match $PI$'s probability of earning 5\% profits on its portfolio, if $PI$ pays $B$ 81.58\% (100\% * (0.765811 + 0.05000)) of its premium revenues. By transferring its portfolio in this manner $PI$ would lock in certain profits of 3.42\% and $B$ is as likely to earn profits of 5\% of PI's premiums as $PI$ was before the transfer. The transfer of risks frpom $PI$ to $B$ benefits both insurers.

Similarly, $NHI$'s probability, $\Phi_{NHI}$(0.752844 = PLR + 1 * 0.002844) is 0.8413, $PI$'s probability of profits of at least 5\%. $NHI$ can match $PI$'s probability of earning 5\% profits on its portfolio, if $PI$ pays $NHI$ 81.28\% (100\% * (0.762844 + 0.05000)) of its premium revenues. By transferring its portfolio in this manner $PI$ would lock in certain profits of 3.72\% and $NHI$ is as likely to earn profits of 5\% of PI's premiums as $PI$ was before the transfer. Once again, the transfer of risks frpom $PI$ to $NHI$ benefits both insurers.

As well, $\Phi_{NHI}$(0.761376 = PLR + 4 * 0.002844) ($\Phi_{B}$(0.813244 = PLR + 4 * 0.015811)) the probability of a PLRE more than four standard errors above the Population Loss Ratio is virtually 0.0000, $NHI$ ($B$) are all but guaranteed to earn profits of 5.14\% () 

\subsection{Loss Adjusted Risk Premiums - PI Transfers Insurance Risks To B Or NHI} \label{sec:LossandRiskAdjustedPremiumsThatWorkTransferstoInsurerBandNHI}

$PI$'s situation is even better if $NHI$ and $B$ have more modest goals: Avoiding losses with $PI$'s pre-transfer probability, 0.9772. All insurers have the same probability that their PLREs will fall below two of their standard errors above the Population Loss Ratio. For $NHI$ this point is 0.755688 and for $B$ this point is 0.781622. If $PI$ pays $NHI$ 75.57\% of its premium revenues, $NHI$ will have the same probability of avoiding a loss, on its entire portfolio, that $PI$ had before the transfer occurred. If $PI$ pays $B$ 78.16\% of its premium revenues, $B$ will have the same probability of avoiding a loss, on its entire portfolio, that $PI$ had before the transfer occurred.

If $B$ accepts 78.16\% of $PI$'s premium revenues in return for accepting $PI$'s claims liabilities, $PI$ locks in profits of 6.84\%. If $PI$ pays $NHI$ 75.57\% of its premium revenues it locks in profits of 9.43\%. Insurers $B$ and $NHI$ will want a greater share of $PI$'s guaranteed profits, but no insurer (risk assuming health care provider) smaller, post-transfer, than $PI$, can assume $PI$'s claims cost liabilities for an amount less than 85\% of $PI$'s premium revenues if they want to earn profits of at least 5\% with $PI$'s pre-transfer probability. 

Previously clinically efficient providers, who accept $PI$'s capitation payments and the responsibility for managing $PI$'s claims become inefficient insurers just by agreeing to capitation contracts. Once they become liable, as insurers, for the variable costs of patient care, they must cut patient care (See Section~\ref{sec:InsurerRiskandMaximumSustainableBenefits}), or face financial ruin. 

Even very generous reinsurance companies will not accept insurance risks, at \emph{affordable} fees, from capitated providers. Reinsurers do not want the risks of high claims costs that $PI$ seeks to avoid by paying providers through capitation. The sole benefit of capitation is that it forces providers, at arm's length, to cut medically necessary and appropriate care for their patients. Low cost, provider reinsurance would reduce, or eliminate, the cuts in medically necessary and appropriate care that capitation compels, eliminating the only thing capitation accomplishes: forcing health care providers to eliminate medically necessary and appropriate care or suffer adverse financial consequences.
